相关论文: Toric arrangement and discrete truncated power

The Compton amplitude subtraction function is an essential component in work concerning both the proton radius puzzle and the proton-neutron mass difference. However, owing to the difficulty in determining the subtraction function, it…

The efficient inversion of matrix polynomials is a critical challenge in computational mathematics. We design a procedure to determine the inverse of matrices polynomial of multidimensional Laplace matrices. The method is based on…

Deletion-restriction is a fundamental tool in the theory of hyperplane arrangements. Various important results in this field have been proved using deletion-restriction. In this paper we use deletion-restriction to identify a class of toric…

We define a combinatorial object that can be associated with any conic-line arrangement with ordinary singularities, which we call the combinatorial Poincar\'e polynomial. We prove a Terao-type factorization statement on the splitting of…

In this lecture we review recent lattice QCD studies of the statistical properties of the eigenvalues of the QCD Dirac operator. We find that the fluctuations of the smallest Dirac eigenvalues are described by chiral Random Matrix Theories…

A toric arrangement is an arrangement of subtori of codimension one in a real or complex torus. The poset of layers is the set of connected components of non-empty intersections of these subtori, partially ordered by reverse inclusion. In…

A poly-log time method to compute the truncated theta function, its derivatives, and integrals is presented. The method is elementary, rigorous, explicit, and suited for computer implementation. We repeatedly apply the Poisson summation…

We explore the mathematical consequences of the assumption of a discrete space-time. The fundamental laws of physics have to be translated into the language of discrete mathematics. We find integral transformations that leave the lattice of…

The polynomial subtraction method, a new numerical approach for reducing the noise variance of Lattice QCD disconnected matrix elements calculation, is introduced in this paper. We use the MinRes polynomial expansion of the QCD matrix as…

This work is a study of polynomial compositions having a fixed number of terms. We outline a recursive method to describe these characterizations, give some particular results and discuss the general case. In the final sections, some…

Several formulas for computing coarse indices of twisted Dirac type operators are introduced. One type of such formulas is by composition product in $E$-theory. The other type is by module multiplications in $K$-theory, which also yields an…

Recently in joint work with E. Sert, we proved sharp boundedness results on discrete fractional integral operators along binary quadratic forms. Present work vastly enhances the scope of those results by extending boundedness to bivariate…

The concept of permutograph is introduced and properties of integral functions on permutographs are established. The central result characterizes the class of integral functions that are representable as lattice polynomials. This result is…

We prove a theorem that allows one to count solutions to determinant equations twisted by a periodic weight with high uniformity in the modulus. It is obtained by using spectral methods of $\operatorname{SL}_2(\mathbb{R})$ automorphic forms…

An effective hamiltonian is derived exactly for the one-dimensional periodic Anderson model via a canonical transformation. The canonical transformation has been calculated up to infinite order, thus an exact transformation was performed in…

A certain truncation of the overlap (domain wall fermions) contains $k$ flavors of Wilson-Dirac fermions. We show that for sufficiently weak lattice gauge fields the effective mass of the lightest Dirac particle is exponentially suppressed…

A group theoretical procedure for parametrizing non-forward matrix elements of non-local QCD operators is introduced. The related (two-variable) distribution amplitudes are given as sum over power corrections of the double distributions.…

Discrete Green's functions are the inverses or pseudo-inverses of combinatorial Laplacians. We present compact formulas for discrete Green's functions, in terms of the eigensystems of corresponding Laplacians, for products of regular graphs…

We define and study the Tutte polynomial of a hyperplane arrangement. We introduce a method for computing it by solving an enumerative problem in a finite field. For specific arrangements, the computation of Tutte polynomials is then…

Virtual quark effects in lattice QCD are studied in an approach where the infrared modes are included in a precise and gauge-invariant manner. At fixed physical volume the required number of modes does not increase in the continuum limit,…